Passengers and crew were taken from the stricken vessel on Wednesday, the coast guard said in a statement, and 27 sustained minor injuries.
Most will be transported to the coastal city of Mokpo while 21 crew members will remain on the ship.
A mistake by the captain or a navigating officer might have caused the accident but the coast guard will conduct a thorough investigation, the organisation's Commissioner General Kim Yong-jin said.
President Lee Jae Myung, who is travelling in the Middle East, ordered details of the rescue operation to be made public as they occurred, Yonhap News Agency reported.
The 26,000-ton ferry Queen Jenuvia 2 was travelling from Jeju Island to Mokpo.
The boat's Mokpo-based operator, Seaworld Ferry, lists the vessel as having a capacity of 1010 passengers as well as lower decks for large vehicles and passenger cars.
A coast guard official said the ferry had struck a rocky island near Jindo.
A loud bang had startled passengers during the night, causing panic and confusion, passenger Kim Namhyun said.
"I thought I might die. The sound was too loud," said Kim, 51, a diving instructor on Jeju Island.
"But having seen the Sewol ferry, I knew that in situations like this, you have to stay calm, move outside, wear a life jacket and wait," Kim said, referring to the sinking of the Sewol ferry in 2014.
Footage showed passengers wearing life vests awaiting transfer to rescue boats.
The vessel's bow appeared stuck on the edge of a small island but looked to be upright and the passengers seemed calm.
Weather conditions were reported to be fair with light winds.
Memories are still fresh in South Korea of the sinking of the Sewol ferry carrying many children on a school trip to Jeju.
The Sewol was sailing from the west coast port of Incheon when it sank near the site of Wednesday's incident although further off the island of Jindo.
The ferry, later found to have been overloaded with cargo and illegally modified to carry more than it was designed for, went into a turn too fast and began listing.
It lay on its side as passengers awaited rescue before sinking as the country watched on live television.
Many victims were found in their cabins, where they had been told to wait while the captain and crew members were rescued by the first coast guard vessels to arrive at the scene.
